Broadband Response and a Transformation between Dual‐ and Single‐Wavelength Detection in Coupled Doped‐Well Quantum Cascade Detector

As a third‐generation infrared detector, the quantum cascade detector (QCD) exhibits an accurately adjustable wavelength, low noise, and ultrafast response characteristics. By introducing an additional doping layer, QCD also shows excellent application prospects in the broadband response. Herein, a coupled doped‐well QCD with an array structure located at very long‐wave infrared (VLWIR, ≈15 µm) is prepared. Based on the energy levels interaction and carrier distribution, the regulatory mechanism of the applied bias on the response characteristics is explored. At zero bias, the detector exhibits dual‐wavelength detection owing to the splitting of the energy levels, then transforms into single‐wavelength detection with the bias increasing. Simultaneously, the QCD device exhibits a broadband response (≈13–16 µm) from 15 to 300 K and an excellent detectivity of 1.52 × 1012 cm Hz1/2 W−1 at 15 K. A high R0A (>106 Ω cm2) and robust detectivity (>109 cm Hz1/2 W−1) are obtained at room temperature. The results of the response characteristics presented in this work provide a strategy for the flexible application of QCD in infrared detection.


Introduction
Quantum cascade detector (QCD), as a photovoltaic device, has made itself one of the prevalent devices in infrared detection. [1][2][3][4][5] Similar to self-powered photodetectors, [6][7][8] the QCD device could operate at zero bias, resulting in low dark current and high signal-to-noise ratio (S/N). [9,10] The difference is that the QCD is an intersubband (ISB) transition device and thus has a faster response time (≈1 ps), although at the cost of quantum efficiency. [11,12] The detection wavelength of QCD could also be controlled easily by tuning the thickness of the doped layer. [1,13] Currently, coupled doped-well QCD demonstrate a broadband response based on the multiple transition path of photoelectron in the active region. [14,15] Furthermore, the special doped-well structure could enable fast longitudinal optical (LO) phonon depopulation (<0.5 ps) of the upper energy level. [3] However, the broadband response QCD has not been fully investigated, especially the complex energy levels interaction in the active region.
Energy levels interaction in the cascade structure is closely related to the performance of the detector, involving the photo electric conversion efficiency, [16,17] electrons migration behavior, [2,7] and dark current, [18,19] etc. For instance, a higher responsivity has been exhibited via adjusting the overlap integral (OI) between the upper energy level and extractor energy level. [3,20] This is ascribed to that the optimized OI improves the extraction efficiency and restricts the backward transfer of electrons. Besides, regulating the oscillator strength is beneficial to optimize the photoelectric conversion efficiency. [11] Generally, the ideal energy levels arrangement could be obtained through the optimal design of the cascade structure. However, the actual condition would deviate from the ideal due to the fluctuation of the layer thickness and chemical component. In addition, the coupling characteristic of the energy levels in the coupled doped-well structure has not been reported. Hence, regulating the energy level arrangement and associating the response performance with energy level coupling is significant to broaden the application of coupled doped-well QCD in infrared detection.
As a third-generation infrared detector, the quantum cascade detector (QCD) exhibits an accurately adjustable wavelength, low noise, and ultrafast response characteristics. By introducing an additional doping layer, QCD also shows excellent application prospects in the broadband response. Herein, a coupled doped-well QCD with an array structure located at very long-wave infrared (VLWIR, ≈15 µm) is prepared. Based on the energy levels interaction and carrier distribution, the regulatory mechanism of the applied bias on the response characteristics is explored. At zero bias, the detector exhibits dual-wavelength detection owing to the splitting of the energy levels, then transforms into single-wavelength detection with the bias increasing. Simultaneously, the QCD device exhibits a broadband response (≈13-16 µm) from 15 to 300 K and an excellent detectivity of 1.52 × 10 12 cm Hz 1/2 W −1 at 15 K. A high R 0 A (>10 6 Ω cm 2 ) and robust detectivity (>10 9 cm Hz 1/2 W −1 ) are obtained at room temperature. The results of the response characteristics presented in this work provide a strategy for the flexible application of QCD in infrared detection.

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Herein, we have fabricated a coupled doped-well QCD with an array structure, which could enable operating under normal incident irradiation. The influence of applied bias and temperature on the response performance of the QCD device is reported. It is found that as the applied bias increases, the detector shows a transformation between dual-and singlewavelength detection. This phenomenon could be ascribed to the carrier redistribution and the decline of energy levels coupling strength under the driving of bias. In addition, a broadband response between 13 and 16 µm is shown from 15 to 300 K due to the energy level splitting. Owing to the limitation of the barrier layer for dark current, the detector also exhibits a responsivity amounts to 1.45 mA W −1 with detectivity of 1.52 × 10 12 cm Hz 1/2 W −1 at 15 K, and maintaining a higher R 0 A (>10 6 Ω cm 2 ) and robust detectivity (>10 9 cm Hz 1/2 W −1 ) at room temperature. Figure 1 presents the microstructural characteristics of the quantum cascade and surface metal array. The coupled doped-well QCD with a sandwich structure was prepared on the GaAs substrate by the molecular beam epitaxy (MBE) technology. The bottom and top regions consist of 400 nm and 200 nm n-type GaAs layers (Si-doped, n = 2.5 × 10 18 cm −3 ), respectively, which are mainly to ensure the transmission and collection of photoelectrons. The core region is composed of a 30 periodic asymmetric well-barrier structure, and the active region is composed of two n-doped GaAs layers and an AlGaAs layer, as marked by the yellow dotted frame in Figure 1a. One period of the core region in Angstroms is 58/99/33/99/60/33/41/47.5/50/50, the underlined thickness values correspond to Al 0.28 Ga 0.72 As barriers while the bold values indicate the uniformly doped layer (n-type, 2 × 10 17 cm −3 ). Note that, the structure parameter of the core region is determined by evaluating the simulation results of the energy level characteristics in the QCD, for example, oscillator strength (OS) and overlap integral (OI), extraction efficiency, etc. In addition, a 6 nm Al 0.28 Ga 0.72 As barrier layer grown on the bottom contact restrains the tunneling injection of the electrons from the contact. Figure 1b shows the morphology of the QCD multilayers observed by transmission electron microscope (TEM). Note that the regular fluctuation of image contrast indicates the alternating growth of the well and barrier layers. As shown in Figure 1c, high-resolution TEM exhibits the crystal orientation and lattice constant based on the zinc blende www.advelectronicmat.de structure. No obvious distinct defect is observed in the cascade structure, which means that the crystal has good growth quality.

Microstructure of Array QCD
Array structure, which serves as an efficient way to optimize the light incident mode and increase the light absorption area, [21][22][23][24] has been applied to the detector by photolithography and wet etching technique. Then the top and bottom electrodes, as a photoelectron transmitter, were deposited by the electron beam evaporation of the Ge/Au/Ni/Au (20/50/15/150 nm) electrode. Thermal annealing (390 °C for 30 s) has been adopted under a nitrogen atmosphere to provide good ohmic contact. The whole array is composed of 30 × 56 units and the area of each unit is 60 × 60 µm 2 . Every array unit is electrically connected by a 10 µm wide electrode to ensure the collection of photoelectrons. Figure 1d,e shows the diagram and top-view scanning electron microscope (SEM) of the array structure, respectively. There are almost no bad spots or defects on the surface of the metal array structure.

Energy Level Structure and Optical Field Distribution
The conduction band profile and wavefunctions are calculated by solving the Schrodinger-Poisson equation with an effective 2-band Kane model, [25] which is given by: where m ‖ and m* denote the effective mass in-plane and in the growth direction, respectively. E and ψ(x,y,z) are the eigen energy and wave functions, respectively. V  (z) is electrostatic potential energy resulting from the space charge effect, which causes the conduction band bending. [26] Herein, V  (z) can be obtained by solving the Poisson equation [27] 1 2 is the permittivity which corresponds to the epitaxial layer composition. n D and n i are the doping concentration and electron sheet density of level i. Owing to the charge neutrality in each period, initially assuming V  (z) = V  (z+L) = 0, until the value of V  , ψ i and E i converge, the band structure of one period is shown in Figure 2a. The significant characteristic of the structure is that the active region is composed of two doped wells. Owing to the interaction between the energy levels in the doped wells, the ground state will split into E 1L (lower ground state) and E 1U (upper ground state), while the excited state split into E 5L (lower excited state) and E 5U (upper excited state). In boundto-bound structures, electrons mainly distribute at the ground state level (E 1 ) according to the Boltzmann distribution law with a thermal equilibrium. Under irradiation, these electrons will absorb photons and transition to the excited state level (E 5 ) to achieve the photo-detection function. Note that, owing to the splitting of the excited state, the extractor level E 4 is located between the E 5L and E 5U . The photoelectrons in the active region can be extracted rapidly by resonance tunneling, which is beneficial to improve the quantum efficiency of the intersubband transition.
Based on the array structure, two absorption modes are mainly considered in the QCD device. One is the surface plasmon resonance of the metal structure, [28,29] and the other one is the random scattering of the photon at the structure edge. [30] Where the former mainly utilizes the interaction between the incident photons and interface electrons to couple the normal incident irradiation into the cascade structure. The cross-section distribution of the optical field in the structure is simulated by FDTD (Figure 2b). The zero point (z-axis) represents the interface of metal array and QCD device, and the thickness of the cascade structure is 1.71 µm, corresponding to the region (z-axis: −2-0 µm) of the simulation results. As the FDTD result exhibited, due to the coupling oscillation between the incident photons and the metal surface electrons, the |E z | 2 is distributed not only in the vertical direction (z-axis, yellow dashed box) but also in the plane orientation of cascade structure (x0y plane, red dashed box). Hence, the normal incident irradiation is successfully coupled in the QCD device by the metal array structure. In addition, the coupling efficiency is mainly dominated by the size and period of the array www.advelectronicmat.de structure. A stronger |E z | 2 as well as the coupling efficiency improvement could be achieved with the optimization of structural parameters.
The band structure and optical field distribution of the QCD device is established by simulation. To obtain the response characteristics of the QCD device, a measurement device for studying the detector under normal incident irradiation has been exhibited in Figure 3a. The layout consists of an array QCD, a closed-cycle cryogenic system, an electrometer to collect electrical signals, and an infrared light source with a monochromator. An infrared lens mounted on the vacuum chamber could guarantee that the QCD device is irradiated under normal incident light. The closed-cycle cryogenic system provides a test platform with temperature control. Figure 3b shows the responsivity characteristics of the coupled doped-well QCD under different applied biases at 15 K. Owing to the level coupling, the coupled doped-well QCD exhibits a broadband response from 13 to 16 µm at zero bias. Where the two peak responses are located at 13.7 µm (90.5 meV) and 15 µm (82.6 meV), which correspond to E 1U -E 5U (92.6 meV) and E 1L -E 5L (81.4 meV) , respectively. Slight deviations can be attributed to the fluctuation of the well-barrier thickness. [10,31] Both of the absorption peaks distribute at the long wave infrared, which is in line with our original design. Consequently, the array QCD based on coupled doped-well structure exhibits a brilliant prospect for the dual-wavelength response, which can also be specifically tuned for the broadband detection application.

Response Characteristics of the QCD Device
Owing to the special structure of the coupled doped-well, a transformation is observed under different applied biases, as shown in Figure 3b. The array QCD device exhibits a dualwavelength detection at zero bias, which agrees with the same type of QCD. [8,9] An obvious single-wavelength detection characteristic located at 14.3 µm is exhibited at 1.5 V and the peak responsivity (R p ) increases from 1.45 to 5.13 mA W −1 (Figure 3c). The full width at half maximum (FWHM) decreases from 2.06 to 0.85 µm with the applied bias increasing. This phenomenon of transformation could be explained as follows. First, with the applied bias increasing, the coupling strength between the energy levels is changing, such as the decline of OI and DME (Figure 4a). As the two doping layers have the same intrinsic parameters, the energy level spacings of E 1U to E 5U and E 1L to E 5L will approach as the coupling strength drops (Figure 4b). Therefore, with the applied bias increasing, the two response peaks gradually come closer. Second, as shown in Figure 4c, electrons tend to be distributed at lower energy level E 1L under the driving of the electron field. The transition path becomes from two-channel model to a single-channel. Then, the device exhibits a single-wavelength detection, where the response peak locates at 14.3 µm is closer to the E 1L to E 5L (85 meV) at 1.5 V. Consequently, regulating the energy level interaction and electron distribution by applied bias, the coupled doped-well detector exhibits a transformation between dual-and singlewavelength detection, which is beneficial to expand the application of QCD in infrared detection.
Based on the coupled doped-well structure, the infrared detector exhibits a broadband response (≈13-16 µm) from 15 to 300 K, as shown in Figure 5a. At room temperature, the QCD device still shows a responsivity, which indicates a robust www.advelectronicmat.de signal-to-noise ratio. The peak responsivity (R p ) of the QCD device is 1.45 mA W −1 and drops to 0.092 mA W −1 at room temperature (Figure 5b). This can be ascribed to that the thermal noise (Johnson noise) of the detector becomes more obvious as the temperature increases, resulting in the decline of R p . Figure 5c exhibits the I-V characteristics under dark condition with different temperatures. The asymmetric feature of the I-V curve originated from the asymmetric well-barrier structure of the QCD device. The resistance R 0 , as a key parameter that governs the Johnson noise of the device, has been calculated by deriving from the slope of the I-V curves. the result of R 0 A (product of resistance and the area of the mesa) is shown in Figure 5d. Compared to the same type of QCD device, [8,32] this detector exhibits a higher R 0 A (>10 6 Ω cm 2 ) in the displayed temperature range, indicating a lower dark current in the cascade structure. In addition, based on the Arrhenius thermal activation model, the activation energy (E a ) for the QCD device about 133 meV is obtained. The E a approaches the transition from ground state E 1 to continuum, eliminating the paths for the dark current generation based on the quantum confinement effect of the barrier layer. [33] Restricting the transition channel of dark current with a thicker barrier is an effective way to improve the R 0 A and S/N.
The specific detectivity D* under normal incidence irradiation is expressed as follows: where R λ is the responsivity, and k B and T are the Boltzmann constant and temperature, respectively. Figure 5e shows the result of D* from 15 K to room temperature. Maximum detectivity reaches 1.52 × 10 12 cm Hz 1/2 W −1 at 15 K and maintains a robust detectivity of 1.27 × 10 9 cm Hz 1/2 W −1 at 300 K. Generally, detectivity is mainly dominated by the dark current and thermal noise in the detector. Owing to the higher R 0 A and optimized cascade structure, superior detectivity has been exhibited in the detector compared to the same type of QCD device. [11,14]

Conclusion
In summary, we report a coupled doped-well QCD with broadband response in VLWIR. The |E z | 2 distribution along x0y plane in the cascade structure is realized through the random scattering and surface plasmon resonance. By applying a bias to regulate the energy levels interaction and carrier transition channel, the QCD device shows a transition from dualwavelength to single-wavelength detection model. In addition, based on the splitting of the coupled energy levels, the detector exhibits a broadband response (≈13-16 µm) from 15 to 300 K. As the migration path of dark current is restricted by the barrier layer, an excellent detectivity (>10 12 cm Hz 1/2 W −1 ) is obtained at 15 K, and a higher R 0 A (≈10 6 Ω cm 2 ) and robust detectivity (≈10 9 cm Hz 1/2 W −1 ) are maintained at room temperature. The response characteristics presented in this work provide a novel strategy to expand the application range of QCD devices in Figure 4. Interaction under different applied biases and electron concentration. a) OI and DME between the coupling energy levels dependence of the applied bias. b) The variation trend of energy level spacings (E 1U to E 5U and E 1L to E 5L ) as the function of applied bias. c) The schematic diagram of the conduction band profile and electron distribution. The red and blue arrows represent the transition from E 1U to E 5U and E 1L to E 5L, respectively. www.advelectronicmat.de infrared detection, such as broadband response, room temperature response, multifunction detection, etc.

Experimental Section
Growth and Characterization: The QCD was grown on GaAs substrate by solid-solid MEB at 605 °C. In situ reflection high energy electron diffractometry (RHEED) and optical pyrometer had been equipped in the epitaxial system, and a quadruple mass spectrometer was used to monitor the growth chamber environment. GaAs layer and AlGaAs layer have the same growth rate of 1 µm h −1 . The substrate rotation speed is set to ≈30 rpm to ensure the vertical uniformity and planer of the single layer thickness. The growth sequence was: GaAs (400 nm, Si-doped, 2.5 × 10 18 cm −3 ), Al 0.28 Ga 0.72 As (6 nm), the core region (30 periods, ≈1700 nm), GaAs (200 nm, Si-doped, 2.5 × 10 18 cm −3 ). After deposition, to evaluate the quality of the cascade structure, the interface characterization was carried out by transmission electron microscope at a 200 kV accelerating voltage.
Device Fabrication: Standard UV photolithography and wet-etching technique was employed to prepare the array structure. A Ge/Au/Ni/Au electrode was deposited by electron beam evaporation, then adopting a thermal annealing (390 °C for 30 s) with nitrogen atmosphere to guarantee the ohmic contact. The surface morphology of metal array structure was performed using a desk-top scanning electronic microscope.
Device Characterization: The QCD device was placed in the vacuum chamber equipped with a closed-cycle cryogenic system. The experimental temperature (15 K, 75 K, 150 K, 220 K, and 300 K) was controlled by adjusting the heating power of the resistor around the cold column. The temperature could reduce to 4.2 K (liquid helium temperature) by the refrigeration system, and accurate temperature control from 4.2 to 300 K could be achieved based on the assembled heating module. An electrometer was used to record the current signal under dark condition and illumination. The I-V characteristic was carried out under different temperatures without illumination. Then, an infrared broadband lamp served as the illumination source and equipped a monochromator to provide a monochromatic source. The incident irradiation power (P λ ) was calibrated with an optical power meter. After that, the responsivity of the QCD device was performed by the test system and the photo-response current was collected by the electrometer. Compared to the measurement method based on Fourier spectrometer and blackbody radiation, this system is simpler and less costly. In addition, the responsivity can be obtained directly rather than by calculating the blackbody responsivity and response spectrum intensity.